Decentralized rigid formation flocking requires a swarm of autonomous agents to maintain a predetermined geometric configuration while moving, relying solely on local sensing and communication. However, existing decentralized control methods struggle to maintain strict inter-agent distance constraints in cluttered environments, often suffering from local minima deadlocks, high frequency control oscillations, or limited flexibility during obstacle navigation, resulting in low success rate. To address these limitations, we propose Rigid Swarm Control (RSC), a decentralized control framework for large-scale rigid formation flocking. To escape local minima via robust long-term planning while ensuring short-term safety, RSC integrates finite-horizon trajectory predictions with a reactive artificial potential field (APF) safety controller within a hybrid architecture. Furthermore, to accelerate formation reassembly after obstacle traversal without interrupting task execution, RSC introduces an online leader-follower reconfiguration mechanism based on stable role exchange. Extensive evaluations in challenging cluttered environments with 25 UAVs demonstrate that RSC reliably unifies rigid formation maintenance, obstacle avoidance, and target tracking. Under strict success criteria - collision-free operation with a maximum relative edge-length error below 10%, RSC achieves an 83% success rate, significantly outperforming existing heuristic and learning-based baselines that fall below 5%.